Reliability Analysis of Concrete Filled Steel Tube Columns by FOSM and Subset Simulation Technique

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 10 | Oct -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 385
RELIABILITY ANALYSIS OF CONCRETE FILLED STEEL TUBE COLUMNS
BY FOSM AND SUBSET SIMULATION TECHNIQUE
Naveen Kumar. S1, Khalid Nayaz Khan2, N.S.Kumar3
1Final Year Student, Department of Civil Engineering, Ghousia college of Engineering, Karnataka, India
2Associate Professor, Department of Civil Engineering, Ghousia college of Engineering, Karnataka, India
3Professor and Director (R&D-Civil Engineering), Department of Civil Engineering, Ghousia college of Engineering,
Karnataka, India
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Abstract - In this study, controlled, deterministic and
reliability found optimal design of concrete filled withcircular
composite columns is entrusted. The main design work is to
attain the nominal load taking ability with the less deflection.
Analytical Study and Reliability analysis of Steel Tube with
concrete filled under monotonic loading is obtained in this
study. Analytical results are fetched by the Finite element
software NASTRAN are verified using ACI-318-1999 code.
Variation may be found to be 20% range accordingly to the
above code.
The reliability technique is directed under the probabilistic
variables such as diameters, thickness, length and grades of
concrete with percentage of glass fibers. FOSM method is used
for the analysis of the results gained. Subset simulation was
adopted for the analysis.
KeyWords: CFST, FOSM, SubsetsimulationTechnique,
Reliability.
1. INTRODUCTION
Concrete-filled steel tube (CFST) sections compriseofa steel
tube in filled with concrete. The solid in fill enhances
compressive properties of the composite section and
decreases the potential for local buckling. Conversely, the
steel tube acts as longitudinal and horizontal supportforthe
concrete infill helping it to resist shear, tension, bending
moment and providing confinement to the concrete.
The steel tube in a concrete filled tubular section (CFST)
offers both longitudinal and lateral support andasa result,it
is subjected to biaxial stresses whereas, concrete is stressed
tri-axially. Concrete filled tubular columns have found their
application as a part of structures and scaffolds.Research on
CFST is being carried out in China since 1970s. CFST has
emerged as a popular structural member because of its
highly desirable structural properties, which include high
strength, stiffness and high ductility. The advantages of the
CFST over other composite members are that the steel tube
gives formwork to the concrete; the in-filled concrete
restrains local buckling of the steel tube.
Reliability is hypothetically characterized as the probability
of achievement as the recurrence of failures or regarding
accessibility, as a probability got from reliability, testability
and maintainability. Testability, maintainability, and
maintenance are regularly characterized as a piece of
"reliability engineering" in Reliability Programs. Reliability
assumes a key part in the cost-viability of systems.
{1-probability failure} = Reliability
 First order second moment method
In this method, the arbitrary factors are described by their
first and second moments. In assessing the first and second
moments of the disappointment work, the first order
estimation is utilized. Therefore this method is called as
FOSM. The FOSM is gotten from Taylors formula for the
extension of a capacity f(x) about a point x.
 Subset simulation technique
Subset simulation technique is a strategy utilized asa partof
reliability models to registering little (i.e., uncommon
occasion) disappointment probabilities experienced in
designing frameworks.
The Monte Carlo simulation (MCS) can give high-reliability
assessment exactness. Be that as it may, the effectiveness of
the unrefined MCS is very low, in substantial part since it is
computationally costly to assess a little disappointment
likelihood. In this paper, subset simulation-based reliability
analysis (SSRA) ways to deal with enhance the
computational effectiveness inreliability-based Optimization
(RBO) issues.

2. EXPERIMENTAL RESULTS
Table -1: Result
Sl
no
D
mm
T
mm
L
mm
fck fy P
1 33.7 2.6 300 23.93 310 118
2 33.7 2.6 300 28.06 310 121
3 33.7 2.6 300 29.01 310 122
4 33.7 3.2 300 23.93 310 132
5 33.7 3.2 300 28.06 310 136
6 33.7 3.2 300 29.01 310 136
7 33.7 4 300 23.93 310 152
8 33.7 4 300 28.06 310 154
9 33.7 4 300 29.01 310 154
10 33.7 5 300 23.93 310 173
11 33.7 5 300 28.06 310 175
12 33.7 5 300 29.01 310 175
13 33.7 6.2 300 23.93 310 176
14 33.7 6.2 300 28.06 310 198
15 33.7 6.2 300 29.01 310 198
16 33.7 7.6 300 23.93 310 220
17 33.7 7.6 300 28.06 310 221
18 33.7 7.6 300 29.01 310 223
19 33.7 9.4 300 23.93 310 246
20 33.7 9.4 300 28.06 310 248
21 33.7 9.4 300 29.01 310 250
22 33.7 11.4 300 23.93 310 269
23 33.7 11.4 300 28.06 310 270
24 33.7 11.4 300 29.01 310 271
25 33.7 13.6 300 23.93 310 285
26 33.7 13.6 300 28.06 310 285
27 33.7 13.6 300 29.01 310 288
3. RELIABILITY ANALYSIS
Limit state function
M = R – S
Where R and S are statistically independent
They are assumed to be regularly disseminated
µm = µR - µS
σM
2= σR
2+ σS
2
Pf = P (M < 0)
=P [(R –S) < 0]
Where Pf = probability of failure
If M= Ordinary variant, then
Pf= 1-Ø(µm/σM)
Reliability index β = µm/ σM
Ø = Cumulative distribution function of the standard
ordinary variant.
3.1 Sample study
The reliability analysis of a CFST column member having
D*t=33.7mm*2.6mm and length of 300mm has been
examined. The material properties are as follows in the in
the employing of the reliability analysis. Compressive
strength of the unconfined concrete (fck) is 28.06N/mm2,
elastic modulus of steel (E) is 2000Gpa and yield strength of
steel (fy) 310N/mm2.
Solving the above parameters by Subset simulation
technique using the COMREL 9 method the reliability index
(β) is -1.522.Their respective probability of failure is found
to be Pf=-0.06426,as we know that reliability for any
structural member subjected to the axial load is R=1-Pf
=93.574%.
Table -2: Reliability Analysis
Sl
no
Pu SST(β) Pf R
R
in%
1 118 -1.405 0.0871 0.9129 91.29
2 121 -1.522 0.0643 0.9357 93.57
3 122 -1.522 0.0643 0.9357 93.57
4 132 -1.504 0.1492 0.8508 85.08
5 136 -1.136 0.1292 0.8707 87.07
6 136 -1.136 0.1292 0.8707 87.07
7 152 -0.900 0.1706 0.8294 82.94
8 154 -0.915 0.1685 0.8314 83.14
9 154 -0.915 0.1685 0.8314 83.14
10 173 -0.619 0.2743 0.7257 72.57
11 175 -0.643 0.2611 0.7389 73.89
12 175 -0.650 0.2547 0.7452 74.52
13 176 -0.559 0.2915 0.7085 70.85
14 198 -0.577 0.2843 0.7156 71.56
15 198 -0.577 0.2843 0.7156 71.56
16 220 -0.429 0.3372 0.6627 66.27
17 221 -0.451 03264 0.6736 67.36
18 223 -0.473 0.3192 0.6808 68.08
19 246 -0.300 0.3821 0.6197 61.97

20 248 -0.348 0.3669 0.6330 63.30
21 250 -0.369 0.3590 0.6409 64.09
22 269 -0.248 0.0871 0.5948 59.48
23 270 -0.269 0.0643 0.6025 60.25
24 271 -0.279 0.0643 0.6125 61.25
25 285 -0.197 0.1492 0.5753 57.53
26 285 -0.212 0.1292 0.5831 58.31
27 288 -1.019 0.1292 0.5753 57.53
4. RESULTS
Following are the results obtained from the L9 taguchi’s
approach with the varying diameters, constant length and
grade of concrete and steel is as per the taguchi’s level-3
approach (TABLE-4) with the 3-factors.
Table: 4 Taguchi’s L 9 Orthogonal array approach
Sl no Pu β(subset
simulation)
Pf Reliability R%
1 118 -1.405 0.087 0.912 91.2
5 136 -1.136 0.129 0.870 87
9 154 -1.136 0.129 0.870 87
11 152 -1.019 0.137 0.866 86.6
15 177 -1.003 0.158 0.741 74.1
16 190 -0.565 0.187 0.712 71.2
21 250 -0.369 0.360 0.640 64
22 269 -0.248 0.406 0.594 59.4
26 285 -0.212 0.417 0.583 58.3
Table: 5 strength/weight ratio obtained from Taguchi’s
method
Sl
no
D
mm
T
mm
Pu Weight Strength
/weight
1 33.7 2.6 118 6.8 17.49
5 33.7 2.6 136 6.8 20.02
9 33.7 2.6 154 6.8 22.73
11 42.4 3.2 152 13.8 11.07
15 42.4 3.2 177 13.8 12.84
16 42.4 3.2 190 13.8 13.79
21 48.3 4 250 22.25 7.93
22 48.3 4 269 22.25 8.65
26 48.3 4 285 22.25 10.11
Fig: 1 Grade of concrete vs Reliability (Dia-33.7mm)
Fig: 2 Diameter vs Reliability
Fig: 3 Taguchi’s method vs Reliability
5. CONCLUSIONS
 The Reliability of member increases with increases in
diameter (Fig:2).
 Because of the load carrying ability mainly depends
upon the strength of the concrete as the grade of
concrete increases the reliability also increases (Fig:1).

 It can be observed from the Fig:3, the maximum
reliability obtained is 93.57% for the T1,G2 and D2
Taguchi’s L9 array combination.
REFERENCES
[1] Ranganathan. R. (1990), “ReliabilityAnalysisandDesign
of Structures” Tata McGraw Hill.
[2] Fred Moses, (1997) „Problems and prospects of
reliability-based optimization‟, Journal of Engineering
Structures, Vol. 19 No. 4 pp. 293-301.
[3] Chethan Kumar. S, Khalid Nayaz Khan and Dr
N.S.Kumar(2016) “Reliability analysis of cft column by
simulation approch” M.Tech dissertation 2016.
[4] Kavya.M.S, Dr. N.S. Kumar & Dr. Mohamed Ilyas Anjum
“Behavior Of Composite Circular Steel Columns In filled
With Fiber ReinforcedConcreteSubjectedToMonotonic
Loading” M.Tech dissertation 2012.
[5] Reliability analysis of a reinforced concrete column
designed according to the Eurocodes.Holický, Milan /
Vrouwenvelder, Ton,IABSE reports = Rapports AIPC =
IVBH Bericht pp251-264.
[6] Ramesh Muthu.D& Dr.N.S.Kumar (2013) “Experimental
Investigation on Concrete Filled Stainless Steel Tubular
(Cfsst) Short Columns under Monotonic Loading”.
M.Tech dissertation 2012.

Reliability Analysis of Concrete Filled Steel Tube Columns by FOSM and Subset Simulation Technique

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Reliability Analysis of Concrete Filled Steel Tube Columns by FOSM and Subset Simulation Technique